Multiple μ-stability analysis of time-varying delayed quaternion-valued neural networks

This article addresses the multiple mu-stability analysis of n-dimensional quaternion-valued neural networks (QVNNs) with unbounded time-varying delays (UTVD) and two general classes of activation functions (AFs). Firstly, the QVNNs are decomposed into four equivalent real-valued systems, and based on the geometrical configuration of the AFs, the state space Hn is divided into 34n disjoint regions. Considering the properties of AFs, several sufficient conditions are derived to ensure the coexistence of 34n equilibria, out of which 24n are locally mu-stable. Moreover, some sufficient conditions for multiple exponential stability, multiple power stability, andmultiple log stability are also derived in this article. Finally, two numerical examples are presented. The first example validates the effectiveness of the proposed theoretical results while the second example illustrates the application of QVNNs on the associative memory, which shows that QVNNs have the ability to reliably retrieve true- color image patterns.